Group #28481825 — subgroups

Subgroups — #28481825

Order 15104.

378 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Dic₁₁₈	C₂	1	1	yes	maximal, characteristic
2	#21422844	C₂	1	1	yes	maximal, characteristic
3	#21422524	C₂	1	2	yes	maximal
4	#21421991	C₂	1	2	yes	maximal
5	C₅₉×#1837	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic
7	C₈×Dic₁₁₈	—	2	1	no	—
8	C₈×Dic₁₁₈	—	2	1	no	—
9	C₈×Dic₁₁₈	C₄	1	2	yes	—
10	C₈×Dic₁₁₈	C₄	1	2	yes	—
11	#16837455	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₅₉⋊C₈	—	2	1	no	—
14	C₂×C₈×Dic₅₉	—	2	1	no	—
15	#16837155	—	2	1	no	—
16	#16837153	—	2	1	no	—
17	#16837132	—	2	4	no	—
18	C₅₉×#423	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#341	—	2	1	no	—
21	C₅₉×#341	—	2	1	no	—
22	C₂²×Dic₁₁₈	Q₈	1	1	yes	characteristic
23	C₂²×C₅₉⋊C₈	—	2	1	no	—
24	C₄×Dic₁₁₈	—	2	1	no	—
25	C₄×Dic₁₁₈	—	2	1	no	—
26	C₄×Dic₁₁₈	C₂×C₄	1	2	yes	—
27	C₄×Dic₁₁₈	D₄	1	2	yes	—
28	C₂×C₄⋊Dic₅₉	Q₈	1	1	yes	characteristic
29	C₂×Dic₅₉⋊C₄	—	2	1	no	—
30	C₂×C₄×Dic₅₉	—	2	1	no	—
31	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
32	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
33	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
34	Dic₅₉⋊C₈	—	2	2	no	—
35	Dic₅₉⋊C₈	—	2	2	no	—
36	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
37	C₄×C₅₉⋊C₈	—	2	2	no	—
38	C₈×Dic₅₉	—	2	2	no	—
39	C₈×Dic₅₉	—	2	2	no	—
40	C₂×M₁₆×C₅₉	—	2	2	no	—
41	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₅₉	—	2	2	no	—
45	C₄⋊C₈×C₅₉	—	2	2	no	—
46	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
50	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
52	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
53	C₂²×Dic₅₉	—	2	1	no	—
54	C₂²×Dic₅₉	—	2	1	no	—
55	C₂×Dic₁₁₈	—	2	1	no	—
56	C₂×Dic₁₁₈	—	2	4	no	—
57	C₂×Dic₁₁₈	C₄⋊C₄	1	2	yes	—
58	M₁₆×C₅₉	—	4	2	no	—
59	M₁₆×C₅₉	—	4	2	no	—
60	C₂×C₈×C₅₉	—	2	2	no	—
61	C₂×C₈×C₅₉	—	2	2	no	—
62	C₂×C₈×C₅₉	—	4	2	no	—
63	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
68	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₅₉	#41	1	1	yes	characteristic
71	C₄⋊Dic₅₉	—	2	1	no	—
72	C₄⋊Dic₅₉	C₄⋊C₄	1	2	yes	—
73	Dic₅₉⋊C₄	—	2	2	no	—
74	Dic₅₉⋊C₄	—	2	2	no	—
75	C₄×Dic₅₉	—	2	2	no	—
76	C₄×Dic₅₉	—	2	2	no	—
77	C₂×C₅₉⋊C₈	—	2	2	no	—
78	C₂×C₅₉⋊C₈	—	4	2	no	—
79	C₂×C₅₉⋊C₈	—	4	2	no	—
80	C₂³×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₅₉	—	2	2	no	—
82	C₂×C₄×C₅₉	—	4	1	no	—
83	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
86	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
88	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₅₉	#135	1	2	yes	—
90	C₂×C₄×C₅₉	#137	1	2	yes	—
91	C₂×Dic₅₉	—	2	4	no	—
92	C₂×Dic₅₉	—	2	2	no	—
93	C₂×Dic₅₉	—	2	2	no	—
94	C₂×Dic₅₉	—	4	2	no	—
95	Dic₁₁₈	—	2	4	no	—
96	Dic₁₁₈	—	2	2	no	—
97	Dic₁₁₈	#108	1	4	yes	—
98	C₈×C₅₉	—	2	1	no	—
99	C₈×C₅₉	—	2	1	no	—
100	C₈×C₅₉	—	2	1	no	—
101	C₈×C₅₉	—	2	1	no	—
102	C₈×C₅₉	—	8	2	no	—
103	C₅₉⋊C₈	—	4	2	no	—
104	C₅₉⋊C₈	—	8	2	no	—
105	#8661	—	59	1	no	maximal, Sylow
106	C₂²×C₅₉	—	2	1	no	—
107	C₂²×C₅₉	—	2	1	no	—
108	C₂²×C₅₉	#380	1	1	yes	characteristic
109	C₂²×C₅₉	#479	1	2	yes	—
110	C₄×C₅₉	—	2	1	no	—
111	C₄×C₅₉	—	2	1	no	—
112	C₄×C₅₉	—	2	1	no	—
113	C₄×C₅₉	#416	1	1	yes	characteristic
114	C₄×C₅₉	#419	1	1	yes	characteristic
115	C₄×C₅₉	C₂×#108	1	2	yes	—
116	C₄×C₅₉	#464	1	2	yes	—
117	Dic₅₉	—	2	4	no	—
118	Dic₅₉	—	4	2	no	—
119	C₂×C₈×Q₈	—	59	1	no	—
120	#1837	D₅₉	1	1	yes	characteristic
121	#1564	—	59	1	no	—
122	#1487	—	59	2	no	—
123	#1301	—	59	2	no	—
124	C₂×C₅₉	—	2	2	no	—
125	C₂×C₅₉	#1805	1	1	yes	characteristic
126	C₂×C₅₉	#1810	1	1	yes	characteristic
127	C₂×C₅₉	#1814	1	1	yes	characteristic
128	C₂×C₄×Q₈	—	59	1	no	—
129	C₈×Q₈	—	59	2	no	—
130	C₈×Q₈	—	59	2	no	—
131	C₈×Q₈	—	118	1	no	—
132	C₈×Q₈	—	118	1	no	—
133	#431	—	59	2	no	—
134	#423	C₂×D₅₉	1	2	yes	—
135	C₂×C₄⋊C₈	—	59	1	no	—
136	C₂×C₄⋊C₈	—	118	1	no	—
137	C₂×C₄×C₈	—	118	1	no	—
138	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
139	#341	—	2	1	no	—
140	#341	—	2	1	no	—
141	#335	—	118	1	no	—
142	#334	—	118	1	no	—
143	Q₈⋊C₈	—	118	4	no	—
144	C₅₉	#8661	1	1	yes	characteristic, complemented, Sylow
145	C₂²×Q₈	—	59	1	no	—
146	C₂×M₁₆	—	2	2	no	—
147	C₂²×C₈	—	118	1	no	—
148	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
149	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
150	C₄×Q₈	—	59	2	no	—
151	C₄×Q₈	—	59	2	no	—
152	C₄×Q₈	—	118	1	no	—
153	C₄×Q₈	—	118	1	no	—
154	C₂×C₄⋊C₄	—	59	1	no	—
155	C₂×C₄⋊C₄	—	118	1	no	—
156	C₂×C₄²	—	118	1	no	—
157	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	2	2	no	—
160	C₄⋊C₈	—	59	2	no	—
161	C₄⋊C₈	—	118	2	no	—
162	C₄⋊C₈	—	118	2	no	—
163	C₄⋊C₈	—	118	1	no	—
164	C₄⋊C₈	—	118	2	no	—
165	C₂²⋊C₈	—	118	2	no	—
166	C₄×C₈	—	118	2	no	—
167	C₄×C₈	—	118	2	no	—
168	C₄×C₈	—	118	2	no	—
169	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
170	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
171	C₄×C₈	D₂₃₆	1	1	yes	characteristic
172	C₄×C₈	D₂₃₆	1	1	yes	characteristic
173	C₂×Q₈	—	59	2	no	—
174	C₂×Q₈	—	118	4	no	—
175	C₂×Q₈	—	118	1	no	—
176	C₂²×C₄	—	118	1	no	—
177	C₂²×C₄	—	118	1	no	—
178	C₂²×C₄	Q₈×D₅₉	1	1	yes	characteristic
179	C₂²×C₄	#11745689	1	1	yes	characteristic
180	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
181	M₁₆	—	4	2	no	—
182	M₁₆	—	4	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	118	2	no	—
187	C₂×C₈	—	236	2	no	—
188	C₂×C₈	—	236	2	no	—
189	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
190	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
191	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
192	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
193	C₄⋊C₄	—	59	2	no	—
194	C₄⋊C₄	—	118	2	no	—
195	C₄⋊C₄	—	118	2	no	—
196	C₄⋊C₄	—	118	1	no	—
197	C₄²	—	118	2	no	—
198	C₄²	—	118	2	no	—
199	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
200	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
201	C₄²	D₄×D₅₉	1	1	yes	characteristic
202	C₄²	#11745687	1	1	yes	characteristic
203	C₂³	#14273703	1	1	yes	characteristic
204	Q₈	—	59	4	no	—
205	Q₈	—	118	4	no	—
206	Q₈	—	118	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	118	4	no	—
210	C₂×C₄	—	118	2	no	—
211	C₂×C₄	—	118	2	no	—
212	C₂×C₄	—	236	2	no	—
213	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
214	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
215	C₂×C₄	#14273685	1	1	yes	characteristic
216	C₂×C₄	#14273698	1	1	yes	characteristic
217	C₂×C₄	#14273702	1	1	yes	characteristic
218	C₂×C₄	#14273707	1	1	yes	characteristic
219	C₂×C₄	#14273747	1	2	yes	—
220	C₂×C₄	#14273757	1	2	yes	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	2	1	no	—
224	C₈	—	2	1	no	—
225	C₈	—	8	2	no	—
226	C₈	—	472	2	no	—
227	C₈	—	236	2	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	#16837259	1	1	yes	characteristic
231	C₂²	#16837706	1	2	yes	—
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	118	4	no	—
236	C₄	—	236	2	no	—
237	C₄	#16837396	1	1	yes	characteristic
238	C₄	#16837410	1	1	yes	characteristic
239	C₄	#108×D₅₉	1	2	yes	—
240	C₄	#16837621	1	2	yes	—
241	C₂	—	2	2	no	—
242	C₂	#21424108	1	1	yes	characteristic
243	C₂	#21424131	1	1	yes	characteristic
244	C₂	#21424151	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₁₁₈

C₂

yes

maximal, characteristic

#21422844

C₂

yes

maximal, characteristic

#21422524

C₂

yes

maximal

#21421991

C₂

yes

maximal

C₅₉×#1837

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₁₈

C₂²

yes

characteristic

C₈×Dic₁₁₈

—

C₈×Dic₁₁₈

—

C₈×Dic₁₁₈

C₄

yes

—

C₈×Dic₁₁₈

C₄

yes

—

#16837455

C₂²

yes

—

C₂×C₄⋊(C₅₉⋊C₈)

C₂²

yes

characteristic

C₂×Dic₅₉⋊C₈

—

C₂×C₈×Dic₅₉

—

#16837155

—

#16837153

—

#16837132

—

C₅₉×#423

C₂²

yes

—

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₅₉×#341

—

C₅₉×#341

—

C₂²×Dic₁₁₈

Q₈

yes

characteristic

C₂²×C₅₉⋊C₈

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

C₂×C₄

yes

—

C₄×Dic₁₁₈

D₄

yes

—

C₂×C₄⋊Dic₅₉

Q₈

yes

characteristic

C₂×Dic₅₉⋊C₄

—

C₂×C₄×Dic₅₉

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

C₂×C₄

yes

—

Dic₅₉⋊C₈

—

Dic₅₉⋊C₈

—

C₂²⋊(C₅₉⋊C₈)

—

C₄×C₅₉⋊C₈

—

C₈×Dic₅₉

—

C₈×Dic₅₉

—

C₂×M₁₆×C₅₉

—

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₅₉

#41

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

C₄⋊C₄

yes

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₄²×C₅₉

C₂²×C₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

#41

yes

characteristic

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₄⋊C₄

yes

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₅₉

#135

yes

—

C₂×C₄×C₅₉

#137

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

#108

yes

—

C₈×C₅₉

—

C₈×C₅₉

—

100

C₈×C₅₉

—

101

C₈×C₅₉

—

102

C₈×C₅₉

—

103

C₅₉⋊C₈

—

104

C₅₉⋊C₈

—

105

#8661

—

maximal, Sylow

106

C₂²×C₅₉

—

107

C₂²×C₅₉

—

108

C₂²×C₅₉

#380

yes

characteristic

109

C₂²×C₅₉

#479

yes

—

110

C₄×C₅₉

—

111

C₄×C₅₉

—

112

C₄×C₅₉

—

113

C₄×C₅₉

#416

yes

characteristic

114

C₄×C₅₉

#419

yes

characteristic

115

C₄×C₅₉

C₂×#108

yes

—

116

C₄×C₅₉

#464

yes

—

117

Dic₅₉

—

118

Dic₅₉

—

119

C₂×C₈×Q₈

—

120

#1837

D₅₉

yes

characteristic

121

#1564

—

122

#1487

—

123

#1301

—

124

C₂×C₅₉

—

125

C₂×C₅₉

#1805

yes

characteristic

126

C₂×C₅₉

#1810

yes

characteristic

127

C₂×C₅₉

#1814

yes

characteristic

128

C₂×C₄×Q₈

—

129

C₈×Q₈

—

130

C₈×Q₈

—

131

C₈×Q₈

—

118

—

132

C₈×Q₈

—

118

—

133

#431

—

134

#423

C₂×D₅₉

yes

—

135

C₂×C₄⋊C₈

—

136

C₂×C₄⋊C₈

—

118

—

137

C₂×C₄×C₈

—

118

—

138

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

139

#341

—

140

#341

—

141

#335

—

118

—

142

#334

—

118

—

143

Q₈⋊C₈

—

118

—

144

C₅₉

#8661

yes

characteristic, complemented, Sylow

145

C₂²×Q₈

—

146

C₂×M₁₆

—

147

C₂²×C₈

—

118

—

148

C₂²×C₈

C₂²⋊D₅₉

yes

characteristic

149

C₂²×C₈

C₂²⋊D₅₉

yes

characteristic

150

C₄×Q₈

—

151

C₄×Q₈

—

152

C₄×Q₈

—

118

—

153

C₄×Q₈

—

118

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

118

—

156

C₂×C₄²

—

118

—

157

C₂×C₄²

C₂²×D₅₉

yes

characteristic

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

118

—

162

C₄⋊C₈

—

118

—

163

C₄⋊C₈

—

118

—

164

C₄⋊C₈

—

118

—

165

C₂²⋊C₈

—

118

—

166

C₄×C₈

—

118

—

167

C₄×C₈

—

118

—

168

C₄×C₈

—

118

—

169

C₄×C₈

C₄×D₅₉

yes

characteristic

170

C₄×C₈

C₄×D₅₉

yes

characteristic

171

C₄×C₈

D₂₃₆

yes

characteristic

172

C₄×C₈

D₂₃₆

yes

characteristic

173

C₂×Q₈

—

174

C₂×Q₈

—

118

—

175

C₂×Q₈

—

118

—

176

C₂²×C₄

—

118

—

177

C₂²×C₄

—

118

—

178

C₂²×C₄

Q₈×D₅₉

yes

characteristic

179

C₂²×C₄

#11745689

yes

characteristic

180

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

181

M₁₆

—

182

M₁₆

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

118

—

187

C₂×C₈

—

236

—

188

C₂×C₈

—

236

—

189

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

190

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

191

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

192

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

193

C₄⋊C₄

—

194

C₄⋊C₄

—

118

—

195

C₄⋊C₄

—

118

—

196

C₄⋊C₄

—

118

—

197

C₄²

—

118

—

198

C₄²

—

118

—

199

C₄²

C₂×C₄×D₅₉

yes

characteristic

200

C₄²

C₂×D₂₃₆

yes

characteristic

201

C₄²

D₄×D₅₉

yes

characteristic

202

C₄²

#11745687

yes

characteristic

203

C₂³

#14273703

yes

characteristic

204

Q₈

—

205

Q₈

—

118

—

206

Q₈

—

118

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

118

—

210

C₂×C₄

—

118

—

211

C₂×C₄

—

118

—

212

C₂×C₄

—

236

—

213

C₂×C₄

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

214

C₂×C₄

C₄⋊C₄×D₅₉

yes

characteristic

215

C₂×C₄

#14273685

yes

characteristic

216

C₂×C₄

#14273698

yes

characteristic

217

C₂×C₄

#14273702

yes

characteristic

218

C₂×C₄

#14273707

yes

characteristic

219

C₂×C₄

#14273747

yes

—

220

C₂×C₄

#14273757

yes

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

225

C₈

—

226

C₈

—

472

—

227

C₈

—

236

—

228

C₂²

—

229

C₂²

—

230

C₂²

#16837259

yes

characteristic

231

C₂²

#16837706

yes

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

118

—

236

C₄

—

236

—

237

C₄

#16837396

yes

characteristic

238

C₄

#16837410

yes

characteristic

239

C₄

#108×D₅₉

yes

—

240

C₄

#16837621

yes

—

241

C₂

—

242

C₂

#21424108

yes

characteristic

243

C₂

#21424131

yes

characteristic

244

C₂

#21424151

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14273698
commutator	C₄²×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1837	C₂
socle	C₂²×C₅₉	#380
prime radical	C₂³×C₅₉	C₂²⋊Q₈
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1837	D₅₉
hypocenter	C₅₉	#8661
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂×C₄

#14273698

commutator

C₄²×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1837

C₂

socle

C₂²×C₅₉

#380

prime radical

C₂³×C₅₉

C₂²⋊Q₈

cosocle

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
144. C₅₉	#8661	semidirect

H ≅ G/N

type

144. C₅₉

#8661

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₈×Dic₁₁₈	2
#21422844	2
#21422524	2
#21421991	2
C₅₉×#1837	2
#8661	59

subgroup

index

C₂×C₈×Dic₁₁₈

C₅₉×#1837

Subgroups — #28481825

Conjugacy classes of subgroups

Complements

Maximal subgroups